What is the Google Map zoom algorithm? - algorithm

Question

I'm working on a map zoom algorithm which change the area (part of the map visible) coordinates on click.
For example, at the beginning, the area has this coordinates :
(0, 0) for the corner upper left
(100, 100) for the corner lower right
(100, 100) for the center of the area
And when the user clicks somewhere in the area, at a (x, y) coordinate, I say that the new coordinates for the area are :
(x-(100-0)/3, y-(100-0)/3) for the corner upper left
(x+(100-0)/3, y+(100-0)/3) for the corner upper right
(x, y) for the center of the area
The problem is that algorithm is not really powerful because when the user clicks somewhere, the point which is under the mouse moves to the middle of the area.
So I would like to have an idea of the algorithm used in Google Maps to change the area coordinates because this algorithm is pretty good : when the user clicks somewhere, the point which is under the mouse stays under the mouse, but the rest of area around is zoomed.
Somebody has an idea of how Google does ?

Answer 1

Lets say you have rectangle windowArea which holds drawing area coordinates(i.e web browser window area in pixels), for example if you are drawing map on the whole screen and the top left corner has coordinates (0, 0) then that rectangle will have values:
windowArea.top = 0;
windowArea.left = 0;
windowArea.right = maxWindowWidth;
windowArea.bottom = maxWindowHeight;
You also need to know visible map fragment, that will be longitude and latitude ranges, for example:
mapArea.top = 8.00; //lat
mapArea.left = 51.00; //lng
mapArea.right = 12.00; //lat
mapArea.bottom = 54.00; //lng
When zooming recalculate mapArea:
mapArea.left = mapClickPoint.x - (windowClickPoint.x- windowArea.left) * (newMapWidth / windowArea.width());
mapArea.top = mapClickPoint.y - (windowArea.bottom - windowClickPoint.y) * (newMapHeight / windowArea.height());
mapArea.right = mapArea.left + newWidth;
mapArea.bottom = mapArea.top + newHeight;
mapClickPoint holds map coordinates under mouse pointer(longitude, latitude).
windowClickPoint holds window coordinates under mouse pointer(pixels).
newMapHeight and newMapWidth hold new ranges of visible map fragment after zoom:
newMapWidth = zoomFactor * mapArea.width;//lets say that zoomFactor = <1.0, maxZoomFactor>
newMapHeight = zoomFactor * mapArea.height;
When you have new mapArea values you need to stretch it to cover whole windowArea, that means mapArea.top/left should be drawn at windowArea.top/left and mapArea.right/bottom should be drawn at windowArea.right/bottom.
I am not sure if google maps use the same algorithms, it gives similar results and it is pretty versatile but you need to know window coordinates and some kind of coordinates for visible part of object that will be zoomed.

Answer 2

Let us state the problem in 1 dimension, with the input (left, right, clickx, ratio)
So basically, you want to have the ratio to the click from the left and to the right to be the same:
Left'-clickx right'-clickx
------------- = --------------
left-clickx right-clickx
and furthermore, the window is reduced, so:
right'-left'
------------ = ratio
right-left
Therefore, the solution is:
left' = ratio*(left -clickx)+clickx
right' = ratio*(right-clickx)+clickx
And you can do the same for the other dimensions.